# Density-functional theory for internal magnetic fields

@article{Tellgren2018DensityfunctionalTF, title={Density-functional theory for internal magnetic fields}, author={Erik I Tellgren}, journal={Physical Review A}, year={2018}, volume={97}, pages={012504} }

A density-functional theory is developed based on the Maxwell--Schr\"odinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and the total magnetic field, which can equivalently be represented as a physical current density. Hence, the theory can be regarded as a physical current-density functional theory and an alternative to the paramagnetic current density-functional theory due to…

## 13 Citations

### Revisiting density-functional theory of the total current density

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2021

It is proved that Diener’s formulation is unfortunately not capable of reproducing the correct ground-state energy and, furthermore, that the suggested construction of a Hohenberg–Kohn map contains an irreparable mistake.

### Kohn-Sham Theory with Paramagnetic Currents: Compatibility and Functional Differentiability.

- MathematicsJournal of chemical theory and computation
- 2019

This article extends Moreau-Yosida regularization to paramagnetic current-density-functional theory, the most common density-functional framework for magnetic field effects, including a well-defined Kohn-Sham iteration scheme with a partial convergence result.

### Kohn–Sham energy decomposition for molecules in a magnetic field

- PhysicsMolecular Physics
- 2018

ABSTRACT We study the total molecular electronic energy and its Kohn–Sham components within the framework of magnetic-field density-functional theory (BDFT), an alternative to current-dependent…

### Density–wave-function mapping in degenerate current-density-functional theory

- Mathematics
- 2018

We show that the particle density, $\rho(\mathbf{r})$, and the paramagnetic current density, $\mathbf{j}^{p}(\mathbf{r})$, are not sufficient to determine the set of degenerate ground-state wave…

### Force balance approach for advanced approximations in density functional theories.

- PhysicsThe Journal of chemical physics
- 2019

This work proposes a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials based on equations of motion of current quantities and is feasible both in the ground-state and the time-dependent settings.

### Benchmarking Density Functional Approximations for Diamagnetic and Paramagnetic Molecules in Nonuniform Magnetic Fields

- ChemistryJournal of chemical theory and computation
- 2021

A more fine-grained classification of molecular systems on the basis of their response to generally nonuniform magnetic fields is proposed and the relation of orientation to different qualitative responses is considered.

### Benchmarking the Accuracy of the Direct Random Phase Approximation and σ-Functionals for NMR Shieldings.

- ChemistryJournal of chemical theory and computation
- 2021

The results show that the accuracy of the computed NMR shieldings using direct RPA is strongly dependent on the density functional theory reference orbitals and improves with increasing amounts of exact Hartree-Fock exchange in the functional.

### Unique continuation for many-body Schr\"odinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian

- Mathematics
- 2019

We prove the strong unique continuation property for many-body Pauli operators with external potentials, interaction potentials and magnetic fields in $L^p_{\rm loc}(\mathbb{R}^d)$, and with magnetic…

### Unique continuation for the magnetic Schrödinger equation

- MathematicsInternational journal of quantum chemistry
- 2020

Abstract The unique‐continuation property from sets of positive measure is here proven for the many‐body magnetic Schrödinger equation. This property guarantees that if a solution of the Schrödinger…

### Hohenberg–Kohn Theorems for Interactions, Spin and Temperature

- MathematicsJournal of Statistical Physics
- 2019

We prove Hohenberg-Kohn theorems for several models of quantum mechanics. First, we show that for possibly degenerate systems of several types of particles, the pair correlation functions of any…

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